Solve for x cube root of 7x = cube root of 15x-40

$\sqrt[3]{7 x} = \sqrt[3]{15 x - 40}$

Step 1

To remove the radical on the left side of the equation, cube both sides of the equation.

${\sqrt[3]{7 x}}^{3} = {\sqrt[3]{15 x - 40}}^{3}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{7 x}$ as ${(7 x)}^{\frac{1}{3}}$ .

${({(7 x)}^{\frac{1}{3}})}^{3} = {\sqrt[3]{15 x - 40}}^{3}$

Simplify the left side.

Simplify ${({(7 x)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(7 x)}^{\frac{1}{3}})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(7 x)}^{\frac{1}{3} \cdot 3} = {\sqrt[3]{15 x - 40}}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(7 x)}^{\frac{1}{3} \cdot 3} = {\sqrt[3]{15 x - 40}}^{3}$

Rewrite the expression.

${(7 x)}^{1} = {\sqrt[3]{15 x - 40}}^{3}$

Simplify.

$7 x = {\sqrt[3]{15 x - 40}}^{3}$

Simplify the right side.

Simplify ${\sqrt[3]{15 x - 40}}^{3}$ .

Factor $5$ out of $15 x - 40$ .

Factor $5$ out of $15 x$ .

$7 x = {\sqrt[3]{5 (3 x) - 40}}^{3}$

Factor $5$ out of $- 40$ .

$7 x = {\sqrt[3]{5 (3 x) + 5 (- 8)}}^{3}$

Factor $5$ out of $5 (3 x) + 5 (- 8)$ .

$7 x = {\sqrt[3]{5 (3 x - 8)}}^{3}$

Rewrite ${\sqrt[3]{5 (3 x - 8)}}^{3}$ as $5 (3 x - 8)$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{5 (3 x - 8)}$ as ${(5 (3 x - 8))}^{\frac{1}{3}}$ .

$7 x = {({(5 (3 x - 8))}^{\frac{1}{3}})}^{3}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$7 x = {(5 (3 x - 8))}^{\frac{1}{3} \cdot 3}$

Combine $\frac{1}{3}$ and $3$ .

$7 x = {(5 (3 x - 8))}^{\frac{3}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$7 x = {(5 (3 x - 8))}^{\frac{3}{3}}$

Rewrite the expression.

$7 x = {(5 (3 x - 8))}^{1}$

Simplify.

$7 x = 5 (3 x - 8)$

Apply the distributive property.

$7 x = 5 (3 x) + 5 \cdot - 8$

Multiply.

Multiply $3$ by $5$ .

$7 x = 15 x + 5 \cdot - 8$

Multiply $5$ by $- 8$ .

$7 x = 15 x - 40$

Step 3

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $15 x$ from both sides of the equation.

$7 x - 15 x = - 40$

Subtract $15 x$ from $7 x$ .

$- 8 x = - 40$

Divide each term in $- 8 x = - 40$ by $- 8$ and simplify.

Divide each term in $- 8 x = - 40$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{- 40}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{- 40}{- 8}$

Divide $x$ by $1$ .

$x = \frac{- 40}{- 8}$

Simplify the right side.

Divide $- 40$ by $- 8$ .

$x = 5$

Solve for x cube root of 7x = cube root of 15x-40

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